Question: Rewrite as a simplified fraction. ${1.5\overline{6} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 156.6666...\\ 10x &= 15.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 141}$ ${x = \dfrac{141}{90}} $ ${x = \dfrac{47}{30}} \text{or} {1 \dfrac{17}{30}}$